模糊判断矩阵的一致性及其性质

针对决策者对有效方案集给出的一类两两方案比较的模糊判断矩阵,从理论上提出关于模糊判断矩阵一致性的定义及其性质,为进一步研究模糊判断矩阵的方案排序等问题奠定了基础。     

模糊互补判断矩阵一致性检验和改进方法研究

针对模糊互补判断矩阵的一致性修正问题,指出了模糊互补判断矩阵一致性修正方法的不足.从模糊一致矩阵传统定义出发,讨论了检验模糊判断矩阵是否满足完全一致性的方法,推导出模糊一致性指标,并给出了模糊判断矩阵一致性改进的方法.从理论上分析了该算法的可行性.这种算法不仅简便实用,而且为专家对原始判断信息进行针对性修正提供了参考依据.

     

三角模糊数互补判断矩阵的一致性及其排序研究

研究三角模糊数互补判断矩阵的性质和排序问题．建立了三角模糊数互反判断矩阵与互补判断矩阵之间的相互转化关系,给出了三角模糊数互补判断矩阵完全一致性、严格强传递性以及弱传递性的概念,并研究了它们之间的关系,论证了完全一致性等定义的合理性,构建了基于最小二乘的三角模糊数互补判断矩阵排序方法．算例分析表明,该方法是可行而有效的。     

区间互补判断矩阵可接受一致性

对区间互补判断矩阵的一致性进行研究,提出一种新的可接受一致性定义,将不满足可接受一致性的矩阵较容易地修正为可接受一致性矩阵.基于凸组合方法,一族明晰数互补判断矩阵的权重向量可被用来求取可接受一致性区间互补判断矩阵的区间权重,并提出了求取可接受一致性区间互补判断矩阵区间权重向量的算法.数值例子显示了所提出的可接受一致性定义以及算法的可行性和有效性.     

模糊互补矩阵的加性一致性阈值仿真

由于事物的不确定性、信息获取的限制、甚至专家知识的局限性,决策者在决策过程中很难用精确数来表示其偏好,而喜欢用模糊语言来表示。当决策者给出的模糊互补判断矩阵不满足加性一致性,加性一致性指标阈值的确定是一个值得研究的问题。一般来说,决策者给出的模糊互补矩阵具满意一致性,且加性一致性模糊互补矩阵一定是满意一致性模糊互补矩阵。MATLAB中计算机仿真方法构造了大量的满意一致模糊互补判断矩阵,通过计算其加性一致性指标值及其概率分布,获取模糊互补矩阵的加性一致性指标的逼近阈值（0.2）。如果模糊互补判断矩阵的加性一致性指标值小于等于0.2,则矩阵是可接受的;否则需要修订。     

基于残缺互补判断矩阵的交互式群决策方法

研究基于残缺互补判断矩阵的群决策问题.首先利用残缺互补判断矩阵的积型一致性,将每个残缺互补判断矩阵拓展为完整的互补判断矩阵(简称拓展互补判断矩阵),并将所有个体拓展互补判断矩阵集成为群体互补判断矩阵;然后基于群体互补判断矩阵与个体拓展互补判断矩阵之间的偏离阈值同决策者进行交互,使得决策者的意见尽可能协调一致;最后给出一种基于残缺互补判断矩阵的交互式群决策方法,并进行了算例分析.     

区间数互补判断矩阵的一致性

研究了区间数互补判断矩阵的一致性;定义了区间数互补判断矩阵的完全一致性、强一致性、一致性和满意一致性的概念;讨论了定义之间的关系;给出了强一致性判别方法以及3种一致性和满意一致性的判别方法.最后用算例验证了所提出方法的有效性和适用性.     

基于信任关系和互补判断矩阵的群决策方法

随着信息和网络技术的不断发展,基于社会网络的群决策问题受到越来越多研究者的关注.针对社会网络环境下模糊互补判断矩阵的群决策问题,研究群体共识调整过程和方案选择方法.首先,融合决策者之间的社会关系、身份地位、知识能力3个方面信息来构建决策者两两之间的信任关系;其次,提出一种尽可能减少元素间共识补偿的共识度度量方法,在此基础上建立基于信任关系的共识调整模型,并从理论上证明该模型的有效性;最后通过信任关系矩阵的特征向量中心度分别求出专家的重要性权重,用以集结专家的偏好信息和对方案进行排序选择,算例分析表明了所提出方法的有效性.     

区间粗糙数互补判断矩阵的两种一致性

区间粗糙数判断矩阵具有在不确定判断中保留部分确定判断的双重特性,然而目前对其研究相对较少,特别是对其一致性的相关研究。为此该文提出了区间粗糙数互补判断矩阵的完全一致性和强一致性的概念以及判断其是否具有完全一致性和强一致性的相关定理。通过算例讨论了内外一致性对于整体一致性的影响,并给出区间粗糙数判断矩阵的完全一致性和强一致性的关系,为区间粗糙数判断矩阵的应用提供一致性理论基础作出相应探讨。     

三角模糊数互补判断矩阵排序的最小方差法

研究偏好信息为三角模糊数互补判断矩阵形式给出的方案排序方法.根据三角模糊数互补判断矩阵完全一致性的概念,建立了一个基于最小方差的非线性规划模型.通过求解该模型,得到三角模糊数互补判断矩阵的权重向量,并利用三角模糊数排序公式对决策方案进行排序.最后通过算例分析表明了所提出的方法是可行而有效的.     

Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP

The lack of consistency in decision making can lead to inconsistent conclusions. In fuzzy analytic hierarchy process (fuzzy AHP) method, it is difficult to ensure a consistent pairwise comparison. Furthermore, establishing a pairwise comparison matrix requires judgments for a level with n criteria (alternatives). The number of comparisons increases as the number of criteria increases. Therefore, the decision makers judgments will most likely be inconsistent. To alleviate inconsistencies, this study applies fuzzy linguistic preference relations (Fuzzy LinPreRa) to construct a pairwise comparison matrix with additive reciprocal property and consistency. In this study, the fuzzy AHP method is reviewed, and then the Fuzzy LinPreRa method is proposed. Finally, the presented method is applied to the example addressed by Kahraman et al. [C. Kahraman, D. Ruan, I. Do?an, Fuzzy group decision making for facility location selection, Information Sciences 157 (2003) 135-153]. This study reveals that the proposed method yields consistent decision rankings from only n − 1 pairwise comparisons, which is the same result as in Kahraman et al. research. The presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy AHP method.     

一种基于区间数判断矩阵的加权AlP群决策方法

针对决策过程中区间数更适合表达决策者对候选方案的偏好程度,基于区间数判断矩阵,综合考虑决策者个体权重,扩展“和积法”,应用“相对熵”的概念,提出了一种加权个体方案权重集结的群体决策方法．该方法将中间结果转化为实数型再进行集结,避免了决策者判断信息的丢失．最后,通过算例说明了该方法的可行性和有效性．     

Methods for fuzzy complementary preference relations based on multiplicative consistency

To improve the consistency of a preference relation is a hot topic in decision making. Wang and Chen (2008) gave a simple method to construct the complete fuzzy complementary preference relation from only n − 1 pairwise comparisons. However, some values may not be in the defined scope and need to be transformed, and thus some original information may be lost in the transformation process. In this paper, we propose a new method to avoid this issue based on the multiplicative consistency of the fuzzy complementary preference relation and apply it to fuzzy Analytic Hierarchy Process (AHP). An example is further given to illustrate our method.     

Linear optimization modeling of consistency issues in group decision making based on fuzzy preference relations

The consistency measure is a vital basis for group decision making (GDM) based on fuzzy preference relations, and includes two subproblems: individual consistency and consensus consistency. This paper proposes linear optimization models for solving some issues on consistency of fuzzy preference relations, such as individual consistency construction, consensus model and management of incomplete fuzzy preference relations. Our proposal optimally preserves original preference information in constructing individual consistency and reaching consensus (in Manhattan distance sense), and maximizes the consistency level of fuzzy preference relations in calculating the missing values of incomplete fuzzy preference relations. Linear optimization models can be solved in very little computational time using readily available softwares. Therefore, the results in this paper are also of simplicity and convenience for the application of consistent fuzzy preference relations in GDM problems.     

基于模糊多属性决策的射孔方案选择模型研究

射孔是油气井的主要完井方式之一,不同的射孔参数对井的产能有不同的影响。射孔方案涉及产能比、相位角、孔密、穿深、孔径、套管强度降低系数等因素,各因素之间互相影响,互相制约,射孔方案的选择中存在一定的模糊性。探讨将模糊多属性决策方法应用于油气井射孔作业,建立射孔方案模糊多属性决策模型,讨论了无偏好及有偏好情况下的射孔决策模型。仿真实例验证了模型的有效性,为射孔作业提供了一种决策依据。     

A novel approach for combination of individual and group decisions based on fuzzy best-worst method

The process of decision-making in an enterprise may either keep the business on track or derail it. Thus, a senior decision maker often use a group of experts as the supportive team to ensure appropriate decisions. The experts often have different expertise level regarding their knowledge, talent, proficiency, and experience. In this study, we first extend the best-worst method based on the linguistic preferences of decision-makers about importance of attributes. These preferences are converted into triangular fuzzy numbers to be utilized in the linear programming model. That is, in contrast with the original best-worst method in which the preferences towards the attributes are crisp, fuzzy preferences are considered in the proposed method to reflect the imprecise comments of experts. Second, we propose a novel group decision making approach based on the fuzzy best-worst method to combine the opinion of senior decision-maker and the opinions of the experts. Indeed, our model helps the senior decision-maker to make a significant trade-off between democratic and autocratic decision-making styles. From sensitivity analyses on two numerical examples, we show that, when there is conflict between senior decision-maker and group of decision-makers, the consistency of group decision-making (democracy) will increase as it tends to individual decision-making (autocracy).     

模糊多准则决策方法研究综述

模糊多准则决策是当前决策领域的一个研究热点,在实际决策中有着广泛的应用.为此,介绍了基于模糊数、直觉模糊集和Vague集的多准则决策方法和语言多准则决策方法的研究现状,定义了直觉梯形模糊数和区间直觉梯形模糊数,扩展了模糊数和直觉模糊集.最后探讨了目前模糊多准则决策要解决的问题和发展方向.     

Group fuzzy AHP approach to embed relevant data on “communicating material”

The amount of data output into our environment is increasing each day, and the development of new technologies constantly redefines how we interact with information. In the context of product life cycle management, it is not uncommon to use intelligent products to ensure an information continuum throughout the product life cycle (e.g., for traceability purposes). Integrating intelligence and information into products themselves is now possible through numerous technologies (RFID, communicating materials). However, these technologies currently have low memory capacities (several kilobytes or megabytes), whereas to product databases are becoming larger and larger (several gigabytes or terabytes). As a result, a data dissemination process is required to determine the relevant information that should be stored on the product. This paper proposes a multiple-criteria decision-making (MCDM) method based on a fuzzy Analytical Hierarchy Process (fuzzy AHP). This method is context-aware and supports the aggregation of opinions from a group of experts. An application is proposed to embed context-sensitive information in a “communicating textile”.